On the unitary dual of the classical Lie groups II. Representations of S O ( n , m ) inside the dominant Weyl Chamber

Susana A. Salamanca-Riba

Compositio Mathematica (1993)

  • Volume: 86, Issue: 2, page 127-146
  • ISSN: 0010-437X

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Salamanca-Riba, Susana A.. "On the unitary dual of the classical Lie groups II. Representations of $SO(n, m)$ inside the dominant Weyl Chamber." Compositio Mathematica 86.2 (1993): 127-146. <http://eudml.org/doc/90213>.

@article{Salamanca1993,
author = {Salamanca-Riba, Susana A.},
journal = {Compositio Mathematica},
keywords = {unitary representation; real reductive Lie group; cohomological parabolic induction; special unipotent representations; irreducible unitary Harish- Chandra module; positive roots; complexified Lie algebra; Zuckerman module; Dirac operator inequality},
language = {eng},
number = {2},
pages = {127-146},
publisher = {Kluwer Academic Publishers},
title = {On the unitary dual of the classical Lie groups II. Representations of $SO(n, m)$ inside the dominant Weyl Chamber},
url = {http://eudml.org/doc/90213},
volume = {86},
year = {1993},
}

TY - JOUR
AU - Salamanca-Riba, Susana A.
TI - On the unitary dual of the classical Lie groups II. Representations of $SO(n, m)$ inside the dominant Weyl Chamber
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 86
IS - 2
SP - 127
EP - 146
LA - eng
KW - unitary representation; real reductive Lie group; cohomological parabolic induction; special unipotent representations; irreducible unitary Harish- Chandra module; positive roots; complexified Lie algebra; Zuckerman module; Dirac operator inequality
UR - http://eudml.org/doc/90213
ER -

References

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  1. [1] A. Borel and N. Wallach: Continuous cohomology, discrete subgroups and representations of reductive subgroups, in Annals of Mathematics Studies Vol. 94, Princeton University Press, 1980. Zbl0443.22010MR554917
  2. [2] S. Salamanca-Riba: On the unitary dual of some classical Lie groups, Compositio Math.68 (1988), 251-303. Zbl0692.22007MR971329
  3. [3] B. Speh and D. Vogan: Reducibility of generalized principal series representations, Acta Math.145 (1980), 227-229. Zbl0457.22011MR590291
  4. [4] D. Vogan: Representations of Real Reductive Lie Groups, Birkhäuser, Boston-Basel- Stuttgart, 1981. Zbl0469.22012MR632407
  5. [5] D. Vogan: Unitarizability of certain series of representations, Annals Math.120 (1984),141-187. Zbl0561.22010MR750719
  6. [6] G. Zuckerman: On Construction of Representations by Derived Functors. Handwritten notes, 1977. 

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